A statistical or probability distribution describes the "shape" of probable values of a specific [[random variable]]. For example a Bernoulli random variable has a Bernoulli distribution. Known distributions have been well-studied by statisticians and have properties that can be looked up in tables, such as their [[expectation]] and [[variance]]. ## Common Distributions - [[Bernoulli distribution]] - 1 trial with success $p$ - [[Binomial distribution]] - $n$ repeated independent Bernoulli trials - [[geometric distribution]] - repeated Bernoulli trials until the first success is obtained, exclusive of the success - [[first success distribution]] - repeated Bernoulli trials until the first success is obtained, inclusive of the success - [[Negative Binomial distribution]] - repeated Bernoulli trials to obtain $r$ successes - [[uniform distribution]] - all values equally likely - [[normal distribution]] - [[standard normal distribution]] - [[Poisson distribution]] - number of events that happen in a certain time period - [[exponential distribution]] - time until an event happens - [[gamma distribution]] - time until $k$ events happen (e.g., repeated exponential random variables) - [[beta distribution]] - flexible distribution with support [0, 1].